Holographic entropy and brane FRW-dynamics from AdS black hole in d5 higher derivative gravity

TL;DR

This paper explores how higher derivative gravity in five dimensions influences the holographic entropy and brane-world cosmology, showing that such corrections modify thermodynamic quantities without disrupting the AdS/CFT correspondence.

Contribution

It demonstrates that higher derivative terms in 5D gravity alter thermodynamic and cosmological parameters while preserving the AdS/CFT duality, and derives the Cardy-Verlinde formula in this context.

Findings

Higher derivative terms modify Hawking temperature, entropy, and Hubble parameter.

Induced brane geometry can be open, flat, or closed FRW universe.

The AdS/CFT duality remains valid despite higher derivative corrections.

Abstract

Higher derivative bulk gravity (without Riemann tensor square term) admits AdS-Schwarzschild black hole as exact solution. It is shown that induced brane geometry on such background is open, flat or closed FRW radiation dominated Universe. Higher derivative terms contributions appear in the Hawking temperature, entropy and Hubble parameter via the redefinition of 5-dimensional gravitational constant and AdS scale parameter. These higher derivative terms do not destroy the AdS-dual description of radiation represented by strongly-coupled CFT. Cardy-Verlinde formula which expresses cosmological entropy as square root from other parameters and entropies is derived in $R^2$ gravity. The corresponding cosmological entropy bounds are briefly discussed.